The following line passes through point $(-9, 6)$ : $y = -\dfrac{5}{8} x + b$ What is the value of the $y$ -intercept $b$ ?
Answer: Substituting $(-9, 6)$ into the equation gives: $6 = -\dfrac{5}{8} \cdot -9 + b$ $6 = \dfrac{45}{8} + b$ $b = 6 - \dfrac{45}{8}$ $b = \dfrac{3}{8}$ Plugging in $\dfrac{3}{8}$ for $b$, we get $y = -\dfrac{5}{8} x + \dfrac{3}{8}$. ${1}$ ${2}$ ${3}$ ${4}$ ${5}$ ${6}$ ${7}$ ${8}$ ${9}$ ${10}$ ${\llap{-}2}$ ${\llap{-}3}$ ${\llap{-}4}$ ${\llap{-}5}$ ${\llap{-}6}$ ${\llap{-}7}$ ${\llap{-}8}$ ${\llap{-}9}$ ${\llap{-}10}$ ${1}$ ${2}$ ${3}$ ${4}$ ${5}$ ${6}$ ${7}$ ${8}$ ${9}$ ${10}$ ${\llap{-}2}$ ${\llap{-}3}$ ${\llap{-}4}$ ${\llap{-}5}$ ${\llap{-}6}$ ${\llap{-}7}$ ${\llap{-}8}$ ${\llap{-}9}$ ${\llap{-}10}$ $(-9, 6)$